Seminars and Colloquia by Series

TBA by Julia Lindberg

Series
Algebra Seminar
Time
Monday, April 27, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Julia Lindberg – Georgia Institute of Technology

TBA

Dynamics of the Nonlinear Schrödinger Equation with an Inverse-Square Potential

Series
PDE Seminar
Time
Tuesday, April 21, 2026 - 14:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xiaoyi Zhang – University of Iowa –

Please Note: Special time and special room

I will discuss our recent works on the nonlinear Schrodinger equation with an inverse square potential. The primary results include the asymptotic properties of solutions with energy below or equal to the energy of the ground state, as well as the uniqueness of the ground state for the inter-critical problems.

Multiscale-Multiphysics Phenomena in Complex Fluids: The Energetic Variational Approaches

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 20, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005 and https://gatech.zoom.us/j/94954654170
Speaker
Chun Liu – Illinois Institute of Technology

Complex fluids are abundant in our daily life. Unlike traditional solids, liquids and the diluted solutions, the model equations for complex fluids continue to evolve with the new experimental evidences and emerging applications. Most of these important properties are due to the coupling and competition between effects from different scales or even from different physical origins/principles. The energetic variational approaches (EnVarA), motivated by the seminal works of Onsager and Rayleigh, are designed to study such systems. In this talk, I will discuss several complex fluid systems, and the associated mathematical issues.

S^1-actions on Moduli Spaces

Series
Geometry Topology Seminar
Time
Monday, April 20, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jiajun Yan – Rice University –

Moduli spaces are central objects in modern topology and geometry, serving as powerful tools for extracting invariants from underlying manifolds. Gauge theory provides a prolific source of such spaces, utilizing techniques from geometry, analysis, and algebra to probe their structure. In this talk, we survey key gauge-theoretic moduli spaces with an emphasis on how $S^1$-actions can be used to study their topological properties. In particular, we apply these methods to hyperkähler ALE spaces, discussing their applications to the McKay correspondence and symplectic and contact homologies.

Local cohomology with support in Schubert varieties of the Grassmannian

Series
Algebra Seminar
Time
Monday, April 20, 2026 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mike Perlman – University of Alabama

Please Note: There will be a pre-seminar at 10:55-11:25 in Skiles 005.

Given a closed subvariety Z in a smooth complex variety X, the local cohomology sheaves with support in Z are holonomic D-modules, and thus have finite filtration with simple composition factors. We determine the D-module structure on local cohomology in the case when X is a Grassmannian and Z is a Schubert variety, including a combinatorial formula describing the composition factors and the weight filtration in the sense of mixed Hodge modules. Upon restriction to the opposite big cell, these calculations recover several previously known results concerning local cohomology with support in determinantal varieties.

An Elementary Introduction to the Kontsevich Integral II

Series
Geometry Topology Working Seminar
Time
Friday, April 17, 2026 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Thang Le – Georgia Tech

This minicourse provides a friendly, step-by-step introduction to the Kontsevich integral. We begin by demystifying the formula and its construction, showing how it serves as a far-reaching generalization of the classical Gauss linking integral. To establish the invariance of the Kontsevich integral, we explore the holonomy of the Knizhnik–Zamolodchikov (KZ) connection on configuration spaces, utilizing the framework of Chen’s iterated integrals. We will then discuss the universality of the Kontsevich integral for both finite-type (Vassiliev) and quantum invariants, culminating in a concrete combinatorial formula expressed through Drinfeld’s associators. Time permitting, we will conclude by constructing the LMO invariant, demonstrating how it functions as a 3-manifold analog of the Kontsevich integral.

Convergence of ergodic averages from an observational viewpoint

Series
School of Mathematics Colloquium
Time
Friday, April 17, 2026 - 11:00 for
Location
Skiles 005 and 006
Speaker
Lai-Sang Young – New York University –

The Birkhoff Ergodic Theorem describes typical behaviors and averaged quantities with respect to an invariant measure. In this talk, I will focus on "observable" events, equating observability with positive Lebesgue measure. From this observational viewpoint, "typical" means typical with respect to Lebesgue measure. This leads immediately to issues for attractors, where all invariant measures are singular. I will present highlights of developments in smooth ergodic theory that address these questions. The theory of physical and SRB measures applies to dynamical systems that are deterministic as well as random, in finite and infinite dimensions (where observability has to be interpreted differently). This body of ideas argue in favor of convergence of ergodic averages for typical orbits. But the picture is a little more complicated: In the last part of the talk, I will discuss some recent work that shows that in many natural settings (e.g. reaction networks), it is also typical for ergodic averages 
to fluctuate in perpetuity due to heteroclinic-like behavior.

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